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BeamCurrentMonitors
AcceleratorBeamDiagnos4csW.Blokland(ORNL)
USPASandUniversityofNewMexicoAlbuquerqueNM,June23‐26,2009
USPAS09atUNM 1AcceleratorandBeamDiagnos4cs
BeamCurrentMonitors
• WhyuseBeamCurrentMonitors?• Howtocoupletothebeam
– Transformer
– Resis4veWallCurrentmonitor– FaradayCups
• Limita4ons:Noise,bandwidth
• Lab
USPAS09atUNM 2AcceleratorandBeamDiagnos4cs
Par4cleAccelerators
One measure of performance: Power • The amount of particles delivered at a certain
energy.
SNSPowerontarget
SNSEnergydeliveredtotarget
USPAS09atUNM 3AcceleratorandBeamDiagnos4cs
Par4cleAccelerators
• How well do you accelerate beam? – What percent of the particles make it to the end
• Effectiveness of acceleration process. E.g. stripping losses 3-5% of beam
– What percent of time are you operational? • Damage to accelerator
– What is the quality of your beam? • Emittance (collider) • Density profile (target) • Position stability • Radio-activation
USPAS09atUNM 4AcceleratorandBeamDiagnos4cs
ChargedBeam
• What is the beam current?
€
Ibeam =qeNt
=qeNl⋅ βc
InanacceleratorthecurrentisformedbyNpar4clesofchargestateqperunitof4metorunitoflengthlandvelocityβ=v/c.
Thebeamisnearlyanidealcurrentsourcewithaveryhighsourceimpedance
• We can measure the beam through the electric and magnetic fields created by the beam.
USPAS09atUNM 5AcceleratorandBeamDiagnos4cs
BeamCurrentStructure
SNSBeamStructure
USPAS09atUNM AcceleratorandBeamDiagnos4cs 6
BeamImagecurrents
• Fastmovingpar4cles(movingE‐field)createanHfield.TheHfieldmovestheE‐fieldinducedimagecharges.
• Athighveloci4esthewallcurrentspectrumisanimage(oppositesign)ofthebeamspectrum:atataspeedof0.5c,approxRMSlengthis90psor1.8GHz
Movingcharge Fastmovingcharge
USPAS09atUNM 7AcceleratorandBeamDiagnos4cs
[5][5]
BeamImagecurrentsIfthewallcurrentmirrorsthebeamcurrentthenthemagne4cfieldoutsidethebeampipeiscancelled:
Isitcompletelycancelled?• Skindepth:thelengthinwhichthefieldsarereducedbya
factorofe(‐8.7dB).At10Mhz,atypical0.794mmstainlesspipeaeenuates53dB.
€
Ampere's Law : H • dl = I∫ and with Ibeam = - Iimage then H • dl = Ibeam + Iimage∫ = 0→ H = 0
€
δ =10 ⋅103
2πρf
with ρ the resistivity and f the frequency
USPAS09atUNM 8AcceleratorandBeamDiagnos4cs
From[2]Webber.
BeamPipeBreak
Nofieldoutsideofbeampipe.Either:
• installdetectorinsidebeampipeor
– Insidebeampipemeansinstalla4oninvacuum• useaceramicbreak
– Ceramicbreakforcesimagecurrenttofindanotherpathanditwilldoso!
USPAS09atUNM AcceleratorandBeamDiagnos4cs 9
Zgap
GapImpedance• Youbeeerdefineyourgapimpedance.Somethingwillalwaysbepresent,suchasa
pathtogroundand
capacitance.
• Zgapiscombina4onofthegap
capacitanceandallexternal
parallelelements
• Gapvoltage
canbegenerateduptobeamvoltage
USPAS09atUNM AcceleratorandBeamDiagnos4cs 10
Zgap
CourtesyofJimCrisp&MikeReid@FNAL
Currenttransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs 11
€
Line current field : B = µ ⋅
Ibeam
2πr a ϕ
Ibeam vout
Β
R
Torus to guide the magnetic field
Measurethebeamcurrentthroughthemagne4cfieldofthebeam.
[1]
Assumethebeamislongenoughtoberegardedasalinecurrent.E.g.SNSRing:250metersfor1usec
€
H ⋅ dl =∫ NpIp + NsIs = Ip +NsIs with Np =1 ⇒
H = (Ip +NsIs) /2πr (1)
Φ = BS∫ dS= µHA = µA(Ip +NsIs) /2πr with A as area (2)
Vs = −Ns ⋅dΦdt
= Is ⋅ Rs (3)
Currenttransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs 12
Vs
Ampere’sLaw:
€
Is ⋅ Rs = −Ns ⋅µA2πr
⋅d(Ip +NsIs)
dt with Ls = Ns
2µA2πr
⇒
dIsdt
+Rs
LsIs = −
1Ns
⋅dIpdt
(4)
Is(iω)Ip (iω)
= −1Ns
⋅iω
(iω + Rs /Ls)
Flux:(thintoroidapproxima4on)
Faraday’sLaw:
Combine(2)and(3):
vs
Ip
Rs
N turns
Ip
Rs Vp
toroid material permeability = µ0µr cross section = A Mean radius = r
Primary winding Np turns
Integration path dl
Is
Secondary winding Ns turns
Laplacerewrite:
Differen4alequa4on:
H
Currenttransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs 13
€
Is(iω)Ip (iω)
=1Ns
⋅iω
(iω + Rs /Ls)
When
€
Ps = Is2Rs =
Ip2
Ns2 Rs €
Is =IpNs
€
iω >> Rs /Ls
Great, we got our transfer function and now we can figure out what the behavior is of our current transformer:
Power: (transferred from beam)
Currenttransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs 14
The inductance plays an important role in the design of transformer. Note that in the calculation for inductance, the geometry of the setup plays and important role as well as the µ and windings.
Inductance of a torus with a square cross section:
€
Φ = BS∫ dS= µHdS
S∫ = µI2πr
ldrrin
rout
∫ =µI2π
l ln routrin
with L = NΦI
then
L =µN 2l2π
ln routrin
and µ = µ0µr
rin
ι
µr
rout
dS
µr can be > 10000.
€
Ls = Ns2Lp
Currenttransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs 15
Too bad there is also a capacitance: we get an LCR circuit:
€
1Z
=1R
+1iωL
+ iωC⇒
Z =iωL
1+ iωL /R − (ωL /R) ⋅ (ωRC)
[1]
LRCProper4es
USPAS09atUNM AcceleratorandBeamDiagnos4cs 16
€
For low frequency : ω << R /L→ Z = iωLFor high frequency : ω >>1/RC→ Z =1/iωCFor mid frequency : R /L <<ω <<1/RC→ Z ≈ R
€
Z =iωL
1+ iωL /R − (ωL /R) ⋅ (ωRC)
log
ωR/L 1/RC
It’sabandpasswitha:− droop4metdroop− rise4metrise
Whatareproper4esofanLRCcircuit?
[5]
Bandpasseffectsonpulseshape
USPAS09atUNM AcceleratorandBeamDiagnos4cs 17
• Rise4metrise:definedasthe4meittakestheamplitudetogofrom10%to90%.• Rise4meconstantτrise:andτrisecorrespondstothe4meforanincreasebye−1=37%.
Rise‐4meanddroop‐4me
USPAS09atUNM AcceleratorandBeamDiagnos4cs 18
€
tdroop =ln0.9 − ln0.1
ω low
=2.197ω low
=2.1972πf low
≈1
3 f lowω low = R /L⇒tlow ≈ 2L /R or tlow ≈ 2τ low with τ low = L /R
€
trise =ln0.9 − ln0.1
ωhigh
=2.197ωhigh
=2.1972πfhigh
≈1
3 fhighωhigh =1/RC⇒
trise ≈ 2RC or trise ≈ 2τ rise with τ rise = RC
• Droop4me
€
A∝ (1− e− t /τ rise )
Add(long)cabletocurrenttransformer:addcableresistance,capacitanceandinductance:
CurrentTransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs 19
€
τ droop = L /(Rf /A +RL ) = L /RL
Ac4veTransformer:useatrans‐impedancecircuittolowertheloadimpedance. €
τ rise = LsCs τ droop = L /(R +RL )
[1]
[1]
Howtodesignacurrenttransformer:• Highsensi4vity‐>lownumberofturns,lowNs
• Highdroop4me‐>highL‐>highµ,highNs
• Fastrise4me‐>lowstraycapacitance
DesignofCurrentTransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs 20€
τ rise = LsCs
€
Vs = IsRs =IbNs
Rs
€
τ droop = Ls /Rs
€
L s =l
2πln rout
rin
⋅µ ⋅ N s
2
€
τ rise = RC withoutcable
withcable
DesignofCurrentTransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs 21
Ac4vetransformer
Passivetransformer
HowtomeasuretheDCcurrent?Thecurrenttransformerdiscussedseesonlychangesintheflux.TheDCCurrentTransformer(DCCT):lookatthemagne4csatura4onofthetorus.
DCCurrentTransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs 22
• Modula4onoftheprimarywindingsforcesthetorusintosatura4ontwicepercycle.• Secondarywindingssensemodula4onsignalandcanceleachother.• ButwiththeIbeam,thesatura4onisshiuedandIsenseisnotzero• Adjustcompensa4oncurrentun4lIsenseiszeroonceagain.
DCTransformerOpera4on,see[1]
DCCurrentTransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs 23
• Modula4onoftheprimarywindingsforcesthetorusintosatura4ontwicepercycle.• Secondarywindingssensemodula4onsignalandcanceleachother.• ButwiththeIbeam,thesatura4onisshiuedandIsenseisnotzero• Adjustcompensa4oncurrentun4lIsenseiszeroonceagain.
Examplebandwidth:DCto20kHz,resolu4on2µA
[1]
24
CurrentMonitorLimita4ons
Limita4ontotransformers:• Thepermeabilityofacorecanbesaturated:specsofmaxBfieldormaxcurrent4meproductI*t,
• Thermalnoise:
• WeissdomainsleadtoBarkhausennoiseiftermina4ngwithhighimpedance(limitforDC‐type)
• Avoidexternalmagne4cfields
• Torusmaterialhasdependencyofµrontemperatureoronmechanicalstress(micro‐phonicpickup)
• Avoidsecondaryelectronsfrombeingmeasured
€
Vn ≈ 4kbTfhighR -> µA range lower limit
USPAS09atUNM AcceleratorandBeamDiagnos4cs
25
BCMTes4ngFixture
USPAS09atUNM AcceleratorandBeamDiagnos4cs
ImagebyM.Kesselman
26
SNSCurrentTransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs
ImagebyM.Kesselman.
LHCFastCurrentTransformer
USPAS09atUNM AcceleratorandBeamDiagnos4cs 27
U.RaichCASFrasca42008BeamDiagnos4cs
DesignbyBNLforSNS
28
COMPONENTSINSIDEHEBTBCMASSEMBLY
USPAS09atUNM AcceleratorandBeamDiagnos4cs
WallCurrentMonitor• Putaresistoroverthegapandmeasureitsvoltage.
USPAS09atUNM AcceleratorandBeamDiagnos4cs 29
R€
Vgap = Rgap ⋅ Ibeam
NoDCinimagecurrent
Vout
WallCurrentMonitor
USPAS09atUNM AcceleratorandBeamDiagnos4cs 30
U.Raich
WallCurrentMonitor
USPAS09atUNM AcceleratorandBeamDiagnos4cs 31
Schema4csofawallcurrentmonitoranditsequivalentcircuit[1]
Nowforthedetails:• Ceramicgaptoavoidworkinginvacuum• Distributedresistors(30to100)forbeamposi4onindependency• Ferriteringsforlowfrequencyresponse• Shieldforgroundcurrentsandnoiseprotec4on
32
Wait,thereismore
LowtoMidbandModel
Iin/n
BroadbandModel
Iin/n
2ζ=√(RL/RL+Rs)((Rs√C/Le+(1/RL)√Le/C)
ωo=√1/(RL/RL+Rs)LeC
Evenaresistorisnotaresistor:
USPAS09atUNM AcceleratorandBeamDiagnos4cs
[4]
[4]
33
FaradayCups
TheFaradayCupdestruc4velyinterceptsthebeam• DCcoupled!(WithjustaresistorthesignalisVout=Ibeam*R)• Lowcurrentmeasurementspossiblee.g.,10pA• Problemwithsecondaryelectrons:
- Uselongcuporvoltagesuppressionormagne4cfield• Ifnotproperlyterminated‐>veryhighvoltage(beampoten4al)• Mustprocessbeampower(SNSfullpower1.4MW)
USPAS09atUNM AcceleratorandBeamDiagnos4cs
[1]
34
FaradayCups
USPAS09atUNM AcceleratorandBeamDiagnos4cs
LowpowerFaradayCup[1] Highpower(1MW)FaradayCup[1]
35
NoiseIssues
USPAS09atUNM AcceleratorandBeamDiagnos4cs
Noisecanbeaproblem!• TherearemanypowerfulnoisesourcesinAccelerators:
- Switchingpowersupplies- Accelera4ngRF- SourceRF
Caseinpoint:- SNSDTLBCM‐>singleendedandinsideacavity(duetospacelimita4ons)
36
NoiseIssues
USPAS09atUNM AcceleratorandBeamDiagnos4cs
NoiseofDTLcurrenttransformer(insidecavity,singleended)
NoisefromRF
Noisefromswitchingpowersupplies
Beam
Grounded
[8]
37
NoiseIssues
USPAS09atUNM AcceleratorandBeamDiagnos4cs
Beam
SCLBeamCurrentMonitor(singleended)
[8]
38
NoiseIssues
USPAS09atUNM AcceleratorandBeamDiagnos4cs
Beeer:CCLBCMoutsideofcavitybuts4llsingleended.
CCLBeamCurrentMonitor(singleended)
Beam
39
NoiseIssues:CommonMode
USPAS09atUNM AcceleratorandBeamDiagnos4cs
Differen4alnoiseonlongtwinaxwithfarendshieldgrounded.Leu:topandboeom,noiseoneithercenterconductorinto50ohms(each20mV/div);center,difference(2mV/div);(mostofresidualsignalduetodigitalscopesubtrac4on).Right:samesignalsfaster4mescale(each20mV/divand1uS/div).From[2]Webber.
Ifnoiseiscoupledintobothwires,wecanrejectit!‐>commonmodenoiserejec4onbytakingthedifference.
Youwilldothisasalabexperiment.
20mV
2mV
20mV
BCMLunch4meSeminar 40
References
[1]ForckP.,“LectureNotesonBeamInstrumenta4onandDiagnos4cs”,JointUniversityAcceleratorSchool,[email protected][2]WebberR.C.,“TutorialonBeamCurrentMonitoring”,BIW2000,pp83‐101.[3]WebberR.C.,“ChargedPar4cleBeamCurrentMonitoringTutorial”,BIW1994,pp3‐23[4]WebberR.C.,“LongitudinalEmieance:AnIntroduc4ontotheConceptandSurveyofMeasurementTechniques,IncludingDesignofaWallCurrentMonitor”BIW1993[5]Denard,J.C.“CERNAcceleratorSchoolonBeamDiagnos4cs”,28May–6June2008,Dourdan.[6]HammondP.,“Electromagne4smforEngineers”,PergamonPress.[7]WatersC.,“CurrentTransformersprovideaccurate,isolatedMeasurements”,PowerConversion&IntelligentMo4on,IssueDecember1986[8]PlumM.,“LANLCurrentMonitorPickupFinalDesignReview”,March2002.[9]EdministerJ.,“Schaum'sOutlineofElectromagne4cs”